This article starts by discussing the concept of ‘inflation hedging’ and provides estimates of ‘inflation betas’ for standard bond and well-diversified equity indices for over 45 countries. We show that such standard securities are poor inflation hedges. Expanding the menu of assets to Treasury bills, foreign bonds, real estate and gold improves matters but inflation risk remains difficult to hedge. We then describe how state-of-the-art term structure research has tried to uncover estimates of the inflation risk premium, the compensation for bearing inflation risk. Most studies, including very recent ones that actually use inflation-linked bonds and information in surveys to gauge inflation expectations, find the inflation risk premium to be sizeable and to substantially vary through time. This implies that governments should normally lower their financing costs through the issuance of index-linked bonds, at least in an ex ante sense. Our findings thus indicate a potentially important role for inflation index linked bonds. We briefly discuss the pros and cons of such bonds, focusing the discussion mostly on the situation in the United States, which started to issue Treasury Inflation Protected Securities (TIPS) in 1997. We argue that it is hard to negate the benefits of such securities for all relevant parties, unless the market in which they trade is highly deficient, which was actually the case in its early years in the United States.